In the last episode of Puella Magi Madoka Magica TV anime, Homura seems to have Madoka's bow. In earlier episodes, she only use guns and bombs, when and how did she get this weapon?
She got her weapon from Madoka.
Q: Did Homura get her weapon from Madoka?
A: The weapon Homura got filled the hole that Madoka left when she couldn't use the bow anymore. [Note: I'm not sure if I got this right, maybe someone who still remembers the details of Madoka's ending properly could fill me in with the details of this]
I think it's because in the new universe, Homura didn't have to use her wish for the sake of saving Madoka. She had no need for time manipulation, so instead of that device, she now has a bow. In the Q&A answer section (as cited in the other answer), it's said the bow was to fill in the hole, being that there is no cause that would have Homura gain the Time Manipulation ability in the new universe.
By searching about this it makes me think, She probably didn't get this from Madoka or whoever it is, She got the bow through her wish as she said "Those are my feelings towards Madoka! That's why, once more, lend me power! Not as the shield that protects Madoka but as the power that smites anyone who threatens her!" since her shield was obtained by wraith.